Details

analyze1.1s (20.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	546	28
1	546	28
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample55.0ms (1%)

Algorithm

1×

intervals

Results

20.0ms	69×	body	1024	valid
14.0ms	136×	body	128	valid
6.0ms	31×	body	512	valid
3.0ms	20×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `difference-of-squares_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`distribute-lft-out--_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

3 → 94

Calls

3 calls:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

series287.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

140.0ms	(/.f64 x (tan.f64 B))
128.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
20.0ms	(/.f64 1 (sin.f64 B))

simplify86.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4891	1413
1	4891	1413

prune94.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Error

0.0b

Counts

105 → 9

Compiler

Compiled 1585 to 658 computations (58.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 x (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64`
4×	`div-exp_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-*l/_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cancel-sign-sub-inv_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

8.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (sin.f64 B))

series282.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
92.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
59.0ms	(/.f64 x (sin.f64 B))
22.0ms	(/.f64 1 (sin.f64 B))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4965	1578
1	4965	1578

prune100.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Error

0.0b

Counts

125 → 7

Compiler

Compiled 2105 to 771 computations (63.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 (cos.f64 B) (sin.f64 B))
0.3b	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`associate-r_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64`
4×	`div-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-r/_binary64` `associate-l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cancel-sign-sub-inv_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

10.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
7.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
4.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

series259.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B))))
93.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
31.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
22.0ms	(/.f64 1 (sin.f64 B))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5032	1670

prune91.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	116	7	123

Error

0.0b

Counts

123 → 7

Compiler

Compiled 2110 to 754 computations (64.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series361.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
86.0ms	(cbrt.f64 x)
82.0ms	(cbrt.f64 x)
82.0ms	(cbrt.f64 x)

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4892	563
1	4892	563

prune67.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Error

0.0b

Counts

92 → 7

Compiler

Compiled 1584 to 574 computations (63.8% saved)

regimes163.0ms (3%)

Accuracy

Total 0.1b remaining (93.9%)

Threshold costs 0.1b (93.9%)

Compiler

Compiled 1465 to 1080 computations (26.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	14
1	26	14

end0.0ms (0%)

sample2.0s (38%)

Algorithm

1×

intervals

Results

664.0ms	2351×	body	1024	valid
307.0ms	3961×	body	128	valid
235.0ms	1140×	body	512	valid
82.0ms	546×	body	256	valid
14.0ms	189×	body	128	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 501 to 372 computations (25.7% saved)

Details

analyze1.1s (20.5%)

sample55.0ms (1%)

simplify14.0ms (0.3%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.6%)

series287.0ms (5.4%)

simplify86.0ms (1.6%)

prune94.0ms (1.8%)

localize9.0ms (0.2%)

rewrite29.0ms (0.5%)

series282.0ms (5.3%)

simplify71.0ms (1.3%)

prune100.0ms (1.9%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series259.0ms (4.8%)

simplify70.0ms (1.3%)

prune91.0ms (1.7%)

localize12.0ms (0.2%)

rewrite15.0ms (0.3%)

series361.0ms (6.8%)

simplify59.0ms (1.1%)

prune67.0ms (1.3%)

regimes163.0ms (3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (38%)

Profiling